Analysing Usain Bolt using GeoGebra/Document: Difference between revisions

The whole story can be read from the estimated velocity time graph – which is a quartic polynomial passing through (0,RT). The GeoGebra screen shows three views. On the left is the main Graphics view showing the scattergram of the data points being well fitted by the blue fifth-degree (quintic) displacement time graph. Superimposed on this are the red velocity-time quartic and the purple acceleration-time cubic graphs. In the upper right corner is the Spreadsheet view. The raw data are in columns B (time) and C (displacement) – and columns D and E hold the transformed data to which the cubic polynomial regression model is fitted. Column F has the distances predicted from our fifth degree displacement-time model. Columns G and H show the corresponding estimates for the velocity and acceleration at the 20m splits. In the bottom right corner is the Graphics 2 View – where we can read the story of the race. The green segment SW on the x-axis represents the clock, and the point T is set up to slide on it. The x-value of T, currently 1.95 s., gives the time elapsed since Bolt left the blocks. The point V on the red graph represents the velocity at the chosen time, currently 9.303 ms^-1. The purple line through V is the tangent to the red graph at V, and its slope, shown in purple represents the acceleration, currently 2.493 ms^-2. The blue shaded area under the curve between S and T is the numerical integral of the red quartic and represents the distance travelled, currently 9.968 metres.